A Hybrid-Filter Approach to Turbulence Simulation

Abstract

Germano (Theor Comput Fluid Dyn 17:225-331, 2004) proposed a hybridfilter approach, which additively combines an LES-like filter operator (F) and a RANS-like statistical operator (E) using a blending function k: H = kF + (1 − k)E. Using turbulent channel flow as an example, we first conducted a priori tests in order to gain some insights into this hybrid-filter approach, and then performed full simulations to further assess the approach in actual simulations. For a priori tests, two separate simulations, RANS (E) and LES (F), were performed using the same grid in order to construct a hybrid-filtered field (H). It was shown that the extra terms arising out of the hybrid-filtered Navier-Stokes (HFNS) equations provided additional energy transfer from the RANS region to the LES region, thus alleviating the need for the ad hoc forcing term that has been used by some investigators. The complexity of the governing equations necessitated several modifications in order to render it suitable for a full numerical simulation. Despite some issues associated with the numerical implementation, good results were obtained for the mean velocity and skin friction coefficient. The mean velocity profile did not have an overshoot in the logarithmic region for most blending functions, confirming that proper energy transfer from the RANS to the LES region was a key to successful hybrid models. It is shown that Germano's hybrid-filter approach is a viable and mathematically more appealing approach to simulate high Reynolds number turbulent flows.

A New Formulation for Hybrid LES-RANS Computations

“…Only the correct, physical, contributions to the derivatives of the flow variables remain and the physical balances in the governing equations are restored. The operators introduced above are essentially equivalent to those of Germano, 13 Hamba, 6, 18 Rajamani and Kim, 14 and Sanchez-Rocha and Menon, 15, 16 because each addresses a specific type of the general blended model discussed here. The relationship between the present work and that of these authors is discussed further later on.…”

“…8,9 Adjustments to the RANS eddy viscosity to accommodate the transition to LES 10,11 have also been proposed, as have models for commutation error 12 and a hybrid formulation based on the blending of RANS and LES filters. [13][14][15][16] While each of these approaches has met with some success, the goal of a general scheme permitting arbitrary placement of LES-RANS transitions to meet the requirements of the flow physics with minimum computational cost remains elusive.…”

Analysis of filtered Navier–Stokes equation for hybrid RANS/LES simulation

“…In fact, for Germano's hybrid filter the ratio of the extra terms to the right-hand side of the filtered Navier-Stokes equation is nearly 33% at the RANS/LES interface region. 27 In the present work, we focus on four typical terms in the transport equation for ū x , where the third term is the extra term for the turbulent stress u x u y ͑=ū x ū y + xy ͒. Figure 3͑b͒ shows the profiles of the rms values of the four terms given by Eq.…”

Investigation of the sensitivity of turbulent closures and coupling of hybrid RANS‐LES models for predicting flow fields with separation and reattachment

“…Some of the methods also include additional treatment at the interface when coupling an upstream RANS region to the downstream LES region [18,20,21] or vice-versa. In the zonal approach, the RANS and LES regions are fixed before the start of the simulation.…”